Iterated primitives of logarithmic powers
Luis A. Medina, Victor H. Moll, Eric S. Rowland
TL;DR
This paper derives closed-form expressions for iterated integrals of logarithmic powers, involving polynomials with harmonic number coefficients, and proves their logconcavity.
Contribution
It provides explicit formulas for iterated primitives of logarithmic powers and establishes the logconcavity of the associated polynomials, advancing understanding of these mathematical objects.
Findings
Closed-form expressions for iterated primitives of logarithmic powers
Polynomials with harmonic number coefficients are involved
Logconcavity of these polynomials is proven
Abstract
The evaluation of iterated primitives of powers of logarithms is expressed in closed form. The expressions contain polynomials with coefficients given in terms of the harmonic numbers and their generalizations. The logconcavity of these polynomials is established.
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